AlgBench: An object-oriented symbolic core system

Abstract

AlgBench is a workbench for the design, implementation and performance measurement of algorithms for symbolic computation, including computer algebra. It provides an interpreter for a symbolic language and a skeleton for implementing data types and algorithms in all areas of symbolic computation. An object-oriented design makes incorporation of new code easy. A compiled implementation language was chosen to allow measurements of efficiency of algorithms and data structures down to machine level.

The interpreter provides a sophisticated scanner and parser for a symbolic functional language. A term rewriting system underlies the evaluator. The evaluator uses the ”infinite evaluation” paradigm. Terms are transformed according to user-defined and built-in rules until no more rules match. In traditional symbolic computation systems this evaluator is a routine that dispatches on the type of the expression. In an object-oriented system this is implemented much cleaner as a virtual method. The pattern matcher and unifier is also implemented in this way. This leads to a transparent design, completely different from traditional systems. It is a strong point-in-case for object-oriented design methodology.

The data types provided are those of a symbolic system: symbols, numbers, and composite expressions (isomorphic to Lisp lists and Mathe-matica expressions). Efficiency is gained by deriving subtypes of these for certain kinds of expressions (e.g. lists, pattern objects, polynomials). This system allows easy implementation and comparison of algorithms. Currently the following are investigated: Parallel/vector arbitrary precision arithmetic, parallel pattern matching, polynomials over finite fields, and interval arithmetic. AlgBench is written in AT&T CH++ V2.0.